Cam mechanism and method for manufacturing the same



Feb. 17, 1953 J. F. JONES ET .AL n 2,628,605

CAM MECHANISM AND METHOD FOR MANUFACTURING THE SAME Filed Nov. 2, 1950 3Sheets-Sheet 1 if; ,L

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Feb. 17, 1953 J. F. JONES ETAL 2,528,605

cAM MEcHANIsM AMD METHOD EoR MANUFACTURING THE sAME /aasa a 7a la fa 4a,5a :a /a a IN V EN TOR.S. )g/f; 7X2 e s. F4557? C? Alk/424mm Feb. 17,1953 ,vous

CAM MECHANISM AND METHOD FOR MANUFACTURING THE SAME' Filed NOV. 2, 19503 Sheets-Sheet 5 Mya/Lx MMA/4 Patented Feb. 17, 1953 CAM MECHANISM ANDMETHOD FOR MANUFACTURING THE SAME John F. Jones, Berkley, and Fred F.Timpner, Birmingham, Mich., and Robert C. Juvinall, Chicago, Ill.,assignors to Chrysler Corporation, Highland Park, Mich., a corporationof Dela- Application November 2, 1950, Serial No. 193,632

This invention relates to cam mechanism and more particularly to camsurface contour and the dimensions to which the contour is formed forproviding smooth and durable performance in service. The instantimprovement is most needed in the valve train of high speed automotiveengines which employ overhead valves, but is not necessarily limited toautomotive engines and high speed cam trains of extended length havingcontrol over the operation of overhead valves.

Cams are traditionally cut to contours developed on the basis ofcircular arcs and straight line tangents in combinations such that thearcs are tangent at each end either to another circular arc or to astraight line tangent. True to be sure, the geometry and calculationsare simple but the resulting behavior of the ordinary cam at high speedsis far from satisfactory where long trains are involved. High ratereturn springs for the cam follower are, of course, necessary to preventbounce under such circumstances and even then other dynamic disturbancesare likely to show up. Moreover, the excessively high rate of spring, towhich resort must be made, is likely to cause pitting and galling at thecam nose owing to the maximum spring force being exerted over what turnsout to be the minimum contact area exposed by the cam during itscycling.

According to a feature of the present invention, a cam is provided inwhich the maximum spring forcer and the maximum unit pressure on the camfacemay be held to allowable limits even though the cam train isrelatively long and operating at high speeds.

4According to another feature, a cam is provided in which theacceleration forces applied to the cam follower are'applied gradually.

According to still another feature of the invention is the provision ofa cam mechanism in which the force necessary to decelerate the inertiaof the train without bounce varies according to the spring forceavailable. That is to say, as contrasted with the traditional practiceof designing the cam and then selecting the spring believed desirablefor the cam, the improved practice makes provision whereby the cam iscontoured to behave according to the operating characteristics of thespring.

Further features, objects, and advantages will either be speciiicalypointed out or become apparent when for a better understanding of theinvention, reference is made to the following detailed description takenin conjunction with the accompanying drawings in which:

5 Claims. (Cl. 123-90) Figures 1 and 3 each show respectively, aconventional cam and the improved cam;

Figures 2 and 4 are charts representing a graphic analysis of thebehavior of the respective conventionalcam and improved cam; and lFigure 5 is a fragmentary view of the improved cam applied to anoverhead valve train.`

As particularly respects Figures 1 and 2, the conventional cam I0 isshown in order that by way of contrast due appreciation may be made ofthe merits of the improved cam later to be described in detail.Conventional cam I0 is provided with a base circle I2 from the surfaceof which there arises a ramp I4 which blends into a ank I6. It is thetraditional function of the ramp I4 to take up the clearance between thecam and its follower and to cause the follower to commence movement at arelatively low constant velocity. Flank I6 may be indicated,l as shownin dotted lines, to have an infinite radius 23 such that the cam isineffect straight-sided in the flank portion. What is preferred thoughas the usual variation in this practice, is for the flank to use afinite radius R such as indicated at 22 for the flank notwithstandingthe fact that the end results approach one another as to the cambehavior. Flank-I6 is tangent to a circular arc nose 20 at the reversalpoint indicated at I8. In the center of the nose at point `2| isindicated the point of maximum lift which may also be called the pointof dwell. Circular arc nose 20 is provided with a constant nose radius24. Point I8, the point of reversal, so called, represents that point atwhich the motion of the follower abruptly undergoes the transition fromacceleration to deceleration and is characterized by the fact that thefollower tends to leave the surface of the cam but for the opposition ofthe follower spring. Follower 2B which cooperates with cam I0 isdiagrammatically represented as adapted for rectilinear motion along theaxis 3U and to be separated from the base circle of the cam by aclearance dimension indicated at 28. Curves 32, 34, and 36 in Figure 2show the cam behavior from the standpoint of lift, velocity, andaccelera.- tion respectively.

The values just enumerated are plotted against degrees of cam openingindicated at 38. In lift curve 32 the ramp portion 40 merges with theflank portion 42 and flank portion 42 inturn merges with nose portion44. The lift behavior for the nose is interrupted in Figure 2 along thedwell axis 45 and the lift curve may be symmetrical on the other side ornot as desirable. The nose portion 44 and, if desirable, the flankportion 42 of curve 32, may comprise cosine waves. In velocity curve 34the nose portion 58 of curve 34 will be seen to follow accordingly asine wave. Flank portion 54 of velocity wave 44 may be either straightor conform to a relatively unpronounced sine wave. It will be noted thatthe ramp portions 4G and'48 in velocity curve 34 are formed such thatthe cam brings the follower up to the velocitv indicated along theconstant velocity portion 48 at a constant rate of change. Inacceleration curve 36, the ramp portions 50 and 52 correspond to theramp portions 4R and 48 to velocitv curve 34. It will be seen in theacceleration curve 36 that for a part oF the ramp travel acceleration isconstant as indicated at 50, and then reduces back to vero at 52throughout the period of constant velocitv of the cam mechanism. Bvconstant velocitv of the mechanism is meant constant' velocitv of travelof the cam follower inasmuch as the calculations here involved are basedon the theory of constant cam rotation. In accelera tion curve 36 aflank portion IR of the cam will be seen to produce a constantacceleration along portion 5R to yield a constant rate of accelerationof value indicated at 68. Since for a given inertia the force necessaryis proportional to the acceleration reouired, it will be seen that thecam train bv conventional design is subiected alnost immediately from noforce to an appreciable accelerating force corresponding value ofacceleration indicated at 68. The reversal point |8 of Figure lcorresponds to the line of reversal 66 'on the acceleration curve 36.The acceleration in this instance drops instantaneously from avalueindicated at l'i8 to the decelerative value of B6. The cam openingforces then are no longer effective andit is the decelerative force ofthe cam train spring which is active to bring about the decelerationthroughout travel across the cam nose. The decelerating portion 60 ofacceleration curve 3G conventionally follows a cosine wave of rather natproportions. As noted previously, since acceleration is in. effect ameasure of force involved, it has been convenient to superimpose curvesof spring resistance in units of force as indicated at 62 and 64. Withproportional coordinates, it may be observed that at all points thecurves 62 for one high rate spring performance and 84 for another highrate spring performance must at all times be spaced from thedecelerating curve 60 in order to prevent valve bounce. It has beenobserved that as the spring rate :is-increased either by virtue of therelatively high inertia of a long valve train or because of the;relatively high speed to which a long valve train must be operated, thespring force curves become more and more steep relative to thecomparatively ilat cosine wave G0. The graphical analysis of Figure 2then will bring out the fact that the excessive force available with therelatively steep curve as shown at 64 attains its maximum value at thetip of the nose of cam I0, notablyat point 2| in Figure 1. tivelysmallest surface area of the cam is active when the tip of the noseis-contacting the cam and with maximum spring force being there exerted,the unit pressures may be expected to reach values such as to causefailure 'and galling in the vicinity ofthe cam nose. Moreover, eventhough-the spring force and the decelerating Iorcenecessary may be nearenough to be compatible, still a broad consideration will show that Yetthe rela- 4 the accelerating and the decelerating forces between curveportions 52 and 56 and curve portions 56 and 60 respectively will tendto cause dynamic disturbances later to show up in phases of the valveoperation particularly in long value train arrangements.

As respects' Figures 3 and 4, the improved cam |00 is provided withportions and 2, which together constitute a ramp |02. The flank isconstituted by portions 3, 4, 5, 6, and 1 and blends with a nose portion|94. The intermediate angles of rotation corresponding to portions l, 2,3, etc. correspond generally with the intermediate angles e1, 412, qu.The follower of the nat face type is indicated at |05 cooperating withthe cam along the instantaneous point of contact |08. Cam |00 isprovided with a base circle radius and a dimension of maximum lift ||2indicated along the dwell YY for the cam. The other principal axis forthe cam XX is seen to be disposed at an angle es with XX axis forfollower |06'. lThe Y'Y axis for follower |06 istheaxis along which cam|66 is adapted for rectilinear movement by action ofV cam 00. Angle Arcpresents portions 5, 6, l, and the nose collectively; the intermediateangles throughout the entire angle i are indicated as 5, qbs, qu, and pawhich range between the limits respectively set at a.,T,T, and 9. inFigure 4, curve |20 corresponds to the lift curve for cam |00. Curve |22corresponds to the velocity curve for cam |00. Curve |24 corresponds tothe acceleration curve for the cam |00. Curve |25 corresponds to therate of change of acceleration of the cam |00, and curve |28 brings outthose points at which the rate of change of acceleration of the cam isconstant. As particularly regards acceleration curve |24 in Figure 4, aspring force curve has been superposed adjacent to it at |34. Bothspring force curve |34 and the acceleration curve portion |24 are shownin a relatively at disposition but such showing is purely forconvenience and the same principle would apply to the spring force curveV of the steeper slope |35. One primary object of the instant inventionbeing to correlate the cam behavoir to the physical behavior of thespring, it is desirable that the force required to decelerate the valvetrain be equal to or less than the force actually exerted by the spring.In equation form, for critical speed this statement may be representedas follows:

As is well known in the art the force required may be readily expressedin equation form thusly:

wenn

FREQ. :Espa

where Wzequivalent weight at valve.

K=spring design factor.

f t)=lift curve at valve, or maximum lift M less instantaneous lift Lv.

Where Bzspring load at maximum lift. R=spring rate lb./in.

aoaaeou" From equations 1, 2, and 3 the value .#(t) :nay be solved forby'diierential equations such as to yield:

where:

"l radan=9 degrees In Figure 3 the sliding point of contact |08 has a Y'coordinate equal to the instantaneous value of lift L. Therefore, y" maybe equated. to the value for L in equation 5:

Since tappet velocity numerically equals the distance of the slidingcontact point |08 from the),

Y'VY' axis the other coordinate for point |08 of value may be expressedas follows:

The coordinates of the point of sliding contact |08 with reference tothe cam axis XX, YY at the angle @sa to axes XX, YY may be formulated asfollows:`

(11) 11:11' sin ps-Hl cos ps Sutable dfferentiatons will yield:

@a dg--n (12) daz-gi tan dda (13) @fr En dwz-dard@ da: 1

Appropriate substitution of the values of the rst and second derivativesEquations l2 and 13 into the general equation for the radius ofcurvature of a curve y=f m) will yield:

Since p, generally Works out greater than one for high speed V*enginework the mlmmum radius of The velocity on: the nose maylbe rewritten inlterms of degrees rather than radians:-

ll' Tr L im ,E ns1 i CLR KW 3N KW N f .l

Acceleration on the nose then is:..

Where es is the instantaneous angularlty of rota? tion vof the cam onthe nose: rSince inertia forces vary with the square of the `speed of amoving object such as a valve train, inertia problems becomeincreasingly importantninhigh speed engine Work; acceleration being adirect measure of the instantly active'inertia forces; it is ofadvantage to have the acceleration increase gradually rather than to beapplied and withdrawn suddenly. It is the function of the ank portion ofthe improved cam of Figures 3 and 4 to accomplish this acceleration'gradually and atA the same timeV to blend smoothly with the noseportionjust discussed. 'The ramp |02 is conventional in that, as is a factlthatcurves |20',v |22, and |24 will bring out, thecam mechanism undergoesconstant acceleration A1 for an instant, then zero acceleration andconstant velocity V2. At some point during the theoretically constantvelocity V2 period the clearance is taken up. As depends on the point atwhich thisrclearance is taken up then, the value for lift at the end ofportion I is:

1 1 (l 8) L1=A1 At the end of portion 2 at constant velocity, the liftis: y

(19) Lz=Vz5z|^Li=Vrin"l-illh2 Portions 3 and 4 bring the cam train tomaximum acceleration in a gradual fashion such that the rate of changeof acceleration on portions 3 and 4 of the cam is constantly increasingat the rate K as is indicated at |39 and is constantly decreasing at therate K xas is indicated at |40 on curve I 26. Hence for portion 3: i

Ka3 't 1,2)954 t KQ'is 't V23 t V22+ /iduz The magnitude of theacceleration A4, velocity V4, and lift L4 at the end of portion 4 arethen readily determinable by assigning real values in Equations 25, 2'7,Vand 29 fOr K, p4, du, V2, and A1 aS appropriate. In accordancewith theplan of the invention, on portion 5 the angle es varies from zero valueto value a; the acceleration A5 is constant and equals acceleration A4at the end of portion 4 previously discussed. Further let the rate ofchange of acceleration decrease constantly at rate K for T degrees onportion 6, and on portion 'l increase constantly at rate K for Tdegrees.

In order then that the acceleration and velocity curves at the end ofportion 'I intersect the 'nose contour, then acceleration Av must equalthe acceleration yielded by Equation 17 for the nose and the Velocity V7must equal the velocity yielded by Equation 16 for the velocity at thenose. Let the final value for the acceleration in Equation 17 berepresented as A7 and the final value for the velocity in Equation 16 beindicated as V1. Let the end value for the nose angle equal 0 degrees:

A value of T is to satisfy the simultaneous Equations 31 and 32 is foundto be:

From Equations and 33:

By appropriate integration:

The angle 0s increasing from zero value to value As to portion 5:

(3s). 4 ,dwg

41) Le:-Kaw/taw(AMM/oma The angle @e increasing from zero value tovaluev T as to portion 1:

The angle p7 increasing from zero value to value T. It will beappreciated that when the assumed values for and 0 satisfy theconditions of Equation 34 for the value a the radius of curvature of thenose portion may be easily computed from Equation 14 inasmuch as theangle'ca in Equation 14 varies from the value zero" to the value 0. Thelift curves for the ramp and flank blending into the nose may be readilycomputed according to the lift curves of the respective portions intowhich the ramp and flank are divided. Equations 18 and 19 yield the liftcurves for the appropriate values of qu and A1 assumed and for theappropriate values of (p2 and V2 assumed. The lift curves for the rstportions of the flank may be determined in accordance with Equations 23and 29 once the values for angles Lpg, K, and 4 are established.Equations 33 and 35 yield respectively the values of T and Ks by meansof which the lift curves for portions 5, 6, and 1 of the flank may becomputed through appropriate substitution in Equations 37, 41, and 45. Acam could then, according to the foregoing limits, behave in the mannerdesired. In particular regard to Figure 5 a cam, according to theinstant invention, is shown in an appropriate setting. Cam |00 andfollower |06 of the flat face type coact to operate a push rod |50 onthe end of which is an adjustable cam tappet 52. Tappet |52 cooperatesWith a rocker arm pivoted about pivot |58 and having arms |54 and |56 ofrelative lengths corresponding to the rocker arm ratio C. Arm |56contacts the end of an overhead valve |60 seating at |62 over the end ofa uld passage |66. The cam mechanism causes opening of valve |60 andvalve seating as occasioned by the action of a valve spring |64. Cam |00is cut to the contours according to the chart ot Figure 4 and willoperate as follows. On the opening side of the cam the behavior isdivided broadly into three categories as best brought out 1n. curve |24.That is, after. the initial ac.

-celeration on the ramp, the valve |6015 opened .'rst at the constantacceleration indicated at |45, which is zero, secondly, at the constantacceleration indicated at p5 which is a constant maximum, and thirdly,along the portion of curve |24 indicated at |46 on the nose, which is ofnegative acceleration or deceleration. During the latter named portion|46, it will be noted that the decelerative value-or force generallyparallels the spring force |34 which is available inasmuch as accordingto Equation 1 foregoing, the cam is cut so as to have such behavior asto the nose portion. In order to prevent dynamic disturbances fromshowing up in the cam trainas, for instance, would be occasioned by pushrod |50 compressing as a spring instantaneously and later expanding suchthat the action of valve |60 does not follow exactly the operation ofactuating cam |00, the transition from zero acceleration portions |45 oncurve |24 to the maximum constant acceleration A4 will be observed to bea grad- -ually acting contour.

change of acceleration is shown at curve |26 in constant but of anegative'character as at |40. It is to be observed that rather than havethe acceleration vary instantaneously from zero vto maximum value as ina conventional cam,

the improved cam |24 manifests the behavior of a gradual transition tomaximum acceleration. This gradual transition is of prime importance.

vOn the decelerating side of the accelerating curve |24, another gradualtransition is effected ,i

from the portion of constant maximum accelthe acceleration throughoutthe portion p6 willA be observed on curve |26 to be constant and`` of anegative character that is minus K slope throughout the portion pv oncurve |24 the rate of change of slope will be observed to be constantand of a positive character plus K. Hence in curve |28 the secondderivative of the acceleration at die will be observed to be constantand the second derivative of the acceleration at qbv will be observed tobe constant. Since the lift formulas were set up on the premise of theacceleration and velocity curves of portion 1 blending in with the nose,a smooth contour will result at the respective points Lv, V7, and A7 oncurves |20, |22 and |24 respectively. The duration of these respectiveportions as best se'en in curve |22, is accurately determined by for--mula such that the angle A is always equal to the sum of the respectiveduration angles a, T, T, and 0. As particularly regards curve |24, sincethe companion portions cpa and 4 and also the companion portions s ander are complementary in the respect that where one is of constant rateof change of acceleration of one character, the other is of constantrate of change of acceleration of the opposite character. The build-upthen from zero acceleration to maximum acceleration and from maximumacceleration to deceleration as indicated by nose portion |46 is gradualand hence the forces applied will be gradual as contrasted with thetheoretical instantaneous application of. these 'same forces in` theconventional cam. Since the lift curves and the curve for the radius ofcurvature of the improved cam are explicit as set forth in theforegoing, the cam'contour may be accurately cut to produce a cam actingin accordance with the behavior graphically shown by the chart of Figure4. Such approach to the problem is of advantage in ironing out dynamicdisturbances, bounce, and coil oscillation as may be manifested whenconventional cams are attempted to be used in the environment of a longoverhead valve train operating at high speeds.

Variations within the spirit and scope of the invention described areequally comprehended by the foregoing description.

What is claimed is: l. Mechanism including a curved cam andfollowercomprising a sliding pair in which the lift isin accordance with thefollowing formula:

Where:

L=Lift at cam.

`1M=Maxirnum lift at valve.

B=Total spring load at maximum valve lift. R=Spring rate.

K :Spring factor.

ifi/:Valve gear equivalent weight.

.N=Engine R. P. M.

s=Cam degreesv from maximum lift. C=Ratio of valve lift to cam lift.

2. A slidingpair comprising a cam and follower 0f which the lift of thelatter varies during a. cycle of the former as corresponds to therotative position thereof, in which each cycle comprises three liftperiods viz., a constantly increasing rate of change of acceleration, aconstantly decreasing rate of change of acceleration, and a relativelyhigh constant acceleration, in whichv the said three periods areobtained by employing a curved .cam' surface and flat faced vfollowercooperating to produce an acceleration whereof the second derivativeyielded is constant during each said period.

3. A sliding pair comprising a cam and follower of which the lift of thelatter varies during a. cycle of the former as corresponds to therotative position thereof, in which each cycle comprises a rising phasecomprising three lift periods viz., -a lift period of constant zeroacceleration. a lift period of constant relatively high acceleration,and a lift period of negative acceleration, and transition periodstherebetween, in which the aforesaid periods are obtained by employing aiiat face on the cam follower in contact with Working arcuate surfaceson the cam whereof the transition portions of the latter tangentiallymerge into the liit period portions cut for the aforesaid lift periodsto produce consecutively adjacent segments of equal duration and amountof eiect, one segment of each pair affording a. change of rate of changeof acceleration at constant increase and the other segment of each pairaffording a change of rate of change of acceleration at constantdecrease.

4. In the method of cam lifting a cam follower included in a train ofvalve gear comprising a normally closed valve connected to the camfollower and a valve spring opposing movement of opening of the valvecaused by the lifting of the cam follower, the improved single stepcomprisking the lifting of the cam followerraccording .to

theY following formula:

where L=1ift at cam.

C=ratioof valve lift to cam lift.

M :Maximum lift.

B=spring load at maximum lift.

R=springrate lb./in.

g=386 in./sec2.

K=spring design factor of safety.

W=equiva1ent weight of valve gear at valve.

s=cam degrees on cam nose from maximum lift increasing in the directionof rotation (negative values on opening side of cam), and

N=engine R. P. M.

so as -to maintain a constant spring factor at all points of the camfollower on the cam nose between point of reversal and point of fulllift and thereby maintain the spring resistance proportionately constantat al1 points.

5. In the method of cam lifting a cam follower included in a train ofvalue gear comprising a normally closed valve connected to the camfollower and a valve springopposing movement to open the valve caused bythe lifting of the cam follower, the improvement comprising the steps ofproviding a cam having a radius of curvature on the nose in accordancewith the general case of the expression:

,Ti 60%)] KW Nr (Rio) (Spring Factor) (Valve. Gear Equiv. Wt.)

60 (1r) (BJP-QM.)

12 andthereby lifting the cam follower by meanszcf rotating the cam nosethercagainst according. to the expression;

L=lift.at cam.

C=ratio of valve lift to camlift.

so as to maintain aA constantspring factor and thereby maintaining thespring resistance exerted directly proportional to the valve geardeceleration.

JOHN F. JONES.

FRED F. TIMPNER.

ROBERT C. JUVINALL REFERENCES CITED The following references areV ofrecord in the file of this patent:

UNITED STATES PATENTS Name Date Walti V Aug. 1,1. 1942 OTHER REFERENCESValve Gear Design by Michael C. Turkish.

Eaton Mfg. Co., Wilcox-Rich Division, Detroit, Michigan, 1946 (Div. 28).

Number

